Mathematics, 13.05.2021 14:20 jacamron

GEOMETRY: ANNUAL SALARIES AND GENDER (PERFORMANCE TASK) ⬛️ STEP 1: ⬛️

◉ . Use the regression calculator or another tool of your choice to
create a scatter plot of the data for men, where the independent variable
is the year since 2000 and the dependent variable is the number of
people (in thousands). Take a screenshot of your scatterplot and paste it
below. If your graph does not include labels, then include a description of
what the axes represent.

➜ (Graph #1).
➜ The x axis represents the number of years since the year
2000 while the y axis represents the number of US citizens
who got a bachelor's degree that year. Note that the number
of US citizens is in thousands.

◉ . Use your calculator to find the regression line y = mx + b for men
where x is the number of years since 2000 and y is the number of men.
Complete the regression equation below.
M(x) =

➜ 20.23x + 516.07.

◉ . Repeat the above steps with the data for women.
Insert a screenshot of the scatterplot for women below.

➜ (Graph #2)
➜ The x axis represents the number of years since the year
2000 while the y axis represents the number of US citizens
who got a bachelor's degree that year. Note that the number
of US citizens is in thousands.

Complete the regression equation below.
F(x) =

➜ 28.67x + 685.99.

⬛️ STEP 2: ⬛️

◉ . Often, social changes, such as education trends, show linear
relationships. How well does a linear model fit the data in this problem?
Justify your answer in terms of the scatterplots and in terms of the data
that the regression calculator gives.

➜ Both have a positive correlation, because they are close to
one. These being 0.983 and 0.991 which are both very close
to 1.

◉ . Using proper units, state the slopes for the functions M and F.

➜ Slope of : 20.233.
➜ Slope of : 28.687.

◉ . Explain what these slopes represent in terms of Americans earning
bachelor degrees.

➜ The slopes represent a greater increase to the amount of
women getting bachelors degrees to men. The slope shows
us that this gap continues to rise.

⬛️ STEP 3: ⬛️

◉ . The functions M and F form a system of linear equations. Use your
graphing calculator to find the solutions to this system graphically. Insert
a screenshot of your graph below.

➜ (Graph #3).

◉ . The solution of the system is:

➜ (-20.12 , 108.96).

◉ . Solve the system again using any algebraic method, such as
substitution or elimination. Show your work step-by-step with clear
notation. Make sure your answer matches the answer you found in the
previous problem.

➜ (Picture #4: step-by-step solving).

◉ . Interpret the solution to the system in terms of Americans earning
bachelor degrees. Recall the opening paragraph: “In the early 1980s,
women first started to outnumber men in college enrollment. Since the
mid-1990s, women have earned more bachelor degrees than men.” State
whether or not you think your results from Steps 3a-3c support the
opening paragraph. Justify your reasoning. If the results do not support it,
explain why this might be.

➜ The solution supports the opening paragraph. When
looking at the graph it shows that in the 1980’s women
started outnumbering men and that gap has increased since
then. The numbers support this because -20 refers to 20
years ago as of 2020 which is 1980.

⬛️ STEP 4: ⬛️

◉ . Use the models for M and F to predict the number of degrees that
will be earned by men and women in the year 2015.

➜ The number of degrees earned by men = 819.
➜ The number of degrees earned by women = 1,116.

GEOMETRY: ANNUAL SALARIES AND GENDER (PERFORMANCE TASK)

⬛️ STEP 1: ⬛️
◉ . Use the regression ca

Answers: 3

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Answers

Answer from: Quest

a) one student is chosen from classroom a, then a student is chosen from classroom b.

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b. this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes. this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes. this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes. this makes them dependent events.

Answer from: Quest

0.6, 3/5, and 6% are the 3 same portion.

but, when they're all changed to a decimal they would equal to 0.6.

hope this , good luck!

Answer from: Quest

part a

answer: a reasonable domain is $0 \le n \le 10$ where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

=====================================

part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

=====================================

part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

f(3) = 12*(1.03)^3

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

f(10) = 12*(1.03)^10

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).

Answer from: Quest

h= 12 inches

step-by-step explanation:

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GEOMETRY: ANNUAL SALARIES AND GENDER (PERFORMANCE TASK) ⬛️ STEP 1: ⬛️

◉ . Use the regr...

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